Check out your local music stores, they usually have someone on staff who can help narrow down the choices for you.

My suggestion would be to go with a powered mixer that is able to connect both Front of House speakers AND monitors (your participants will thank you). I would also opt for a mixer with some on-board digital effects (at least a little reverb is nice). Size and power will depend on the number of inputs you think you need and the size of the room. If playing with a drummer, you will probably need a bit more oomph than the smaller portable systems IMO. Lots of choices out there at various price points. Mackie, Yamaha, Peavey...

Get some speaker stands for the front of house speakers to get the sound over crowd level and reaching the folks in the back.

I've been using Behringer DI's for a few years with no real issues, though "purists" will tell you they are junk, tone-sucking etc. Hey, they're affordable and they work. If your budget allows, go with Radial... they make excellent DI's.